Method and device for determining the capacity of a heat exchanger

ABSTRACT

A method and arrangement for determining the capacity of a heat exchanger is provided. The effective heat transfer coefficient for the heat exchanger is calculated from the measured inlet and outlet temperatures of the product and the measured inlet and outlet temperatures of the auxiliary medium. By means of the value, the outlet temperature of the product set for maximum flow of the auxiliary medium is determined as that at which the change in the heat content of the product is at least approximately the same as the change in the heat content of the auxiliary medium and the amount of heat transmitted by the heat exchanger for the product flow. The value is displayed to the user and permits a decision as to how much longer the heat exchanger can reliably be operated.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the US National Stage of International ApplicationNo. PCT/EP2005/004657, filed Apr. 29, 2005 and claims the benefitthereof. The International Application claims the benefits of Germanapplication No. 102004021423.9 DE filed Apr. 30, 2004, both of theapplications are incorporated by reference herein in their entirety.

FIELD OF INVENTION

The invention relates to a method and a device for determining thecapacity of a heat exchanger by means of which the temperature of aproduct flowing through the heat exchanger is to be changed with the aidof an auxiliary medium that serves as a cooling or heating medium.

BACKGROUND OF INVENTION

Heat exchangers of this type are frequently used in process-engineeringinstallations alongside a plurality of different installation componentssuch as, for example, machines, containers, chemical reactors, steamgenerators, columns or pumps. A heat exchanger is in principle a pipethrough which a product that is to be cooled or heated by thesurrounding medium, which is called the auxiliary medium, flows. Factorsdetermining the capacity of the heat exchanger include as large aspossible a heat-exchange area and as large as possible a heat transfercoefficient. Certain requirements for the heat exchanger emerge from thematerials used, for example, the type of product and auxiliary medium,the necessary cooling or heating capacity, the cooling procedure used,structural conditions or legal regulations, for example with regard tocleaning. Because of the different requirements, many different forms ofheat exchangers are widespread, for example, direct-current andcounter-current heat exchangers, tube-bundle-type heat exchangers orplate-type heat exchangers.

A major problem in the operation of heat exchangers is what is known asfouling. Here, fouling is a collective term for contamination of allkinds. Fouling changes the heat transfer coefficient between theauxiliary medium which serves as a cooling or heating medium and theproduct. The consequences of this are that more cooling medium orheating medium is required as auxiliary medium, that the operating costsrise and/or that in the extreme case the desired temperature of theproduct can no longer be set by the heat exchanger. If this extreme caseoccurs, an unscheduled shutdown of the process-engineering installationin which the heat exchanger is used can be caused as a result. A commonremedial measure is therefore a regular shutdown of production for themaintenance and cleaning of heat exchangers. However, this increasesoperating costs and restricts the availability of the installation.

SUMMARY OF INVENTION

An object of the invention is to create a method and a device thatenable early detection of a decline in the capacity of a heat exchanger.

To achieve this object, a method and device are provided in theindependent claims. Further developments of the invention are describedin the dependent claims.

The invention has the advantage that the effects of changed heattransfer coefficients on the operation of the heat exchanger aredetermined and displayed in such a clear manner that they can even beinterpreted correctly by non-specialists. The determined and displayedoutlet temperature of the product which would be set for maximum flow ofthe auxiliary medium provides a particularly clear variable for theuser, as the heat exchanger is being operated here at its capacitylimit. It makes it clear how increasing fouling diminishes theadjustment range available. It is thus easy for the user to recognizewhether and for how much longer the heat exchanger can set a desiredtemperature of a product and can continue to be operated trouble-free ina process-engineering installation. Unforeseen installation downtimescan thus largely be avoided.

A further development of the method has the advantage that the methodfor determining the outlet temperature of the product set for maximumflow of the auxiliary medium can be used in an arithmetically simple andeasy manner for various types of heat exchangers.

In the further development, the arithmetic mean of the values of theoutlet temperature of the product in the subset of value pairs canadvantageously be calculated as a statistical criterion for selecting avalue pair. In this way, a particularly simple, reliable and clearmethod for selection is applied.

A calculation and display of the standard deviation of the values of theoutlet temperature of the product in the subset of value pairs has theadvantage that evidence is obtained about the reliability of the result.The smaller the standard deviation the more meaningful the result fordetermining the capacity of the heat exchanger.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention and embodiments and advantages are explained below indetail with the aid of the drawings, in which an exemplary embodiment ofthe invention is shown.

FIG. 1: shows a schematic diagram of a heat exchanger and

FIG. 2: shows a display for illustrating the capacity of a heatexchanger.

DETAILED DESCRIPTION OF INVENTION

There are heat exchangers of a wide variety of different designs,depending on the conditions in which they are used. The basic structureof a heat exchanger is shown in FIG. 1.

A heat exchanger 1 consists, in accordance with FIG. 1, of a container 2into which a product flows through an inlet 3 and out of which it flowsagain through an outlet 4. The direction of flow of the product ismarked by an arrow 6. Located in the container 2 is a coiled pipe 7through which an auxiliary medium flows in the direction of an arrow 8.In the event of the product being cooled by the heat exchanger 1,cooling water, for example, flows through the pipe 7. The auxiliarymedium enters the heat exchanger 1 by an inlet 9 and exits again by anoutlet 10. The inlet temperature θ_(K,Ein) of the auxiliary medium isrecorded by means of a temperature measuring transducer 11, and theoutlet temperature θ_(K,Aus) by means of a temperature measuringtransducer 12. Correspondingly, the inlet temperature θ_(W,Ein) of theproduct is measured by means of a temperature measuring transducer 13and the outlet temperature θ_(W,Aus) by means of a temperature measuringtransducer 14. Furthermore, to determine the flow F_(K) of the auxiliarymedium through the pipe 7 and the flow F_(W) of the product through thecontainer 2, flowmeters 15 and 16 are provided. By means of a regulatingvalve 17, the flow of the auxiliary medium can be adjusted such that adesired outlet temperature is set for the product. The regulating valve17 receives an actuating signal from a control device 18 to which themeasured values of the measuring transducers 11 . . . 16 are routed asinput signals. Besides their function of calculating the position of theregulating valve 17 as a function of the measured values of themeasuring transducers 11 . . . 16, the control device additionally hasthe function of an evaluation device which, to determine the capacity ofthe heat exchanger 1, determines the outlet temperature of the productset for maximum flow of the auxiliary medium. In a process-engineeringinstallation, the control device 18 is implemented for example in anautomation device which is linked via a data communication network tothe measuring transducers 11 . . . 16 and the regulating valve 17. Thedetermined outlet temperature and further values which are helpful inthe assessment of the capacity of the heat exchanger 1 by a user, canthen be displayed with the aid of a faceplate 19, i.e. by means of adisplay window for process visualization on an operating and monitoringconsole. If too sharp a reduction in the capacity of the heat exchanger1 is displayed, the user can instigate suitable measures to eliminatethe problem at a point in time before a desired outlet temperature ofthe product can no longer be set and thus before a correct flow of theprocess in which the heat exchanger is used would no longer beguaranteed.

The manner in which the capacity of the heat exchanger 1 is determinedby the control device 18, which on account of its additional function isalso called an evaluation device 18, will be explained below.

The outlet temperature θ_(W,Aus) of the product and the outlettemperature θ_(K,Aus) of the auxiliary medium can lie only in a definedrange which is limited by the inlet temperature θ_(W,Ein) of the productand the inlet temperature θ_(K,Ein) of the auxiliary medium. If, forexample, a product is to be cooled down, then the outlet temperatureθ_(W,Aus) of the product cannot become less than the inlet temperatureθ_(K,Ein) of the auxiliary medium. Likewise, the outlet temperatureθ_(K,Aus) of a cooling medium cannot become greater than the inlettemperature θ_(W,Ein) of the product. The temperature range between thetwo inlet temperatures θ_(K,Ein) and θ_(W,Ein) in which values of theoutlet temperatures θ_(K,Aus) and θ_(W,Aus) can physically meaningfullybe set is, as it were, scanned for the calculation with the outlettemperatures θ_(K,Aus) and θ_(W,Aus) of the auxiliary medium and of theproduct, in that the two outlet temperatures are initially set to theinlet temperature θ_(K,Ein) of the auxiliary medium and then graduallyincreased up to the inlet temperature θ_(W,Ein) of the product.Expressed mathematically, this corresponds for example to n valuesθ_(K,Aus,i) with i=1 to n, where θ_(K,Aus,i)=θ_(K,Ein) andθ_(K,Aus,n)=θ_(W,Ein) or m values θ_(W,Aus,j) with j=1 to m, whereθ_(W,Aus,l)=θ_(K,Ein) and θ_(W,Aus,m)=θ_(W,Ein) Or in a differentnotation:

-   θ_(K,Ein) . . . θ_(K,Aus,i) . . . θ_(W,Ein)-   θ_(K,Ein) . . . θ_(K,Aus,j) . . . θ_(W,Ein)

Furthermore, all the pairs of values (θ_(K,Aus,i), θ_(W,Aus,j)) of thetwo outlet temperatures are formed that are mathematically possible. Inthis way, a plurality of value pairs, namely n×m where i=1 to n and j=1to m, are obtained which, based on the above consideration, aremathematically possible. For these value pairs, the amounts of heattransmitted at maximum flow of the auxiliary medium are calculated. Theevaluation takes into account the fact that in the stationary condition,due to the energy balance being in equilibrium, a change {dot over(Q)}_(W) in the energy content of the product is the same as a change{dot over (Q)}_(K) in the energy content of the auxiliary medium and isthe same as the amount of heat {dot over (Q)} transmitted by the heatexchanger. The amount of heat transmitted is thus calculated in threedifferent ways.

The change {dot over (Q)}_(W) in the heat content of the product iscalculated from the temperature difference between inlet temperatureθ_(W,Ein) and outlet temperature θ_(W,Aus,j) of the product, the currentmass flow {dot over (M)}_(W,Aktuell) of the product and the specificheat cp_(W) of the product:{dot over (Q)} _(W) =cp _(W) ·{dot over (m)}_(W,Aktuell)·(θ_(W,Ein)−θ_(W,Aus,j))

Here, the mass flow m_(W,{dot over (A)}Aktuell) can be determined in asimple manner as the product of the flow F_(W), measured by means of theflowmeter 16, and the density of the flowing product.

The change {dot over (Q)}_(K) in the heat content of the auxiliarymedium is calculated from the temperature difference between inlettemperature θ_(K,Ein) and outlet temperature θK_(K,Aus,i) of theauxiliary medium, the maximum possible mass flow {dot over (m)}_(K,Max)and the specific heat cp_(K) of the auxiliary medium:{dot over (Q)} _(K) =cp _(K) ·{dot over (m)}_(K,Max)·(θ_(K,Aus,i)−θ_(K,Ein)).

To calculate the quantity of heat transmitted, firstly the currentlyeffective heat transfer coefficient k_(wirk) is determined from thecurrent measured values of the measuring transducers 11 . . . 16. Thefollowing equation applies to the example of a counter-current heatexchanger:

$k_{wirk} = \frac{{cp}_{W} \cdot \delta_{W} \cdot F_{W} \cdot \left( {\vartheta_{W,{Ein}} - \vartheta_{W,{Aus}}} \right)}{A \cdot \frac{{\Delta\vartheta}_{a} - {\Delta\vartheta}_{b}}{\ln\;\frac{{\Delta\vartheta}_{a}}{{\Delta\vartheta}_{b}}}}$with Δθ_(a)=θ_(W,Ein)−θ_(K,Aus) and Δθ_(b)=θ_(W,Aus)−θ_(K,Ein.)

Here, A denotes the effective exchange area of the heat exchanger andδ_(W) the specific density of the product.

This equation applies in cases where the variables are nottemperature-dependent or pressure-dependent. Otherwise, this can betaken into account in the calculation to increase accuracy.

The amount of heat transmitted {dot over (Q)} is calculated from themean temperature difference between product and auxiliary medium, theheat transfer coefficient k_(wirk) and the effective exchange area Aaccording to the following equation:

$\overset{.}{Q} = {{{k \cdot A \cdot {\Delta\vartheta}_{\ln}}\mspace{14mu}{with}\mspace{14mu}{\Delta\vartheta}_{\ln}} = \frac{{\Delta\vartheta}_{a} - {\Delta\vartheta}_{b}}{\ln\frac{{\Delta\vartheta}_{a}}{{\Delta\vartheta}_{b}}}}$whereby for the mean temperature difference in the case of acounter-current heat exchanger:Δθ_(a)=Δθ_(W,Ein)−θ_(K,Aus) and Δθ_(b)=Δθ_(W,Aus)−θ_(K,Ein)is used, and for the mean temperature difference in a direct-currentheat exchanger:Δθ_(a)=Δθ_(W,Ein)−θ_(K,Ein) and Δθ_(b)=Δθ_(W,Aus)−θ_(K,Aus).

Once the three transmitted amounts of heat {dot over (Q)}_(W), {dot over(Q)}_(K) and {dot over (Q)} have been calculated for each of the valuepairs, those value pairs are sorted out which, based on a comparison ofamounts of heat, are physically appropriate. In the stationarycondition, the three calculated amounts of energy must be equal inmagnitude. This means in cases of cooling that the change {dot over(Q)}_(W) in the heat content of the product must, through heat transfer{dot over (Q)}, produce a corresponding change {dot over (Q)}_(K) in theheat content of the auxiliary medium. Due to measurement errors andsimplifications in the calculation, a certain tolerance has to beallowed for in the calculated values:{dot over (Q)} _(K) ≈Q _(W) {dot over (≈)}{dot over (Q)}.

This equation can basically be solved analytically. It is, however, moreeasily and simply transferable to other forms of heat exchangers todetermine a subset from the plurality of value pairs in which thecalculated values lie within a predeterminable tolerance using thecalculated changes in heat contents and the calculated value of theamount of heat transmitted. The last-mentioned equation thus correspondsto a “filter” by means of which the physically appropriate value pairscan be sorted out as a subset from the plurality of mathematicallypossible value pairs.

Where there is a broad predetermined tolerance, the subset of valuepairs is correspondingly larger so that it is advantageous to selectusing a statistical method a value pair which is highly probable tocontain the outlet temperatures set for maximum flow of the auxiliarymedium. As a particularly simple statistical method, the arithmetic meanof the values of outlet temperatures of the product which are containedin the value pairs of the subset is calculated for this purpose. Toassess the accuracy of this result, the standard deviation of the valuesof the outlet temperatures of the product is determined from this subsetas well as the minimum value and the maximum value of the outlettemperature of the product. If these values are relatively large, thisindicates a comparatively inaccurate result. Where the standarddeviation is relatively small or where the minimum and maximum value lieclose together, it can be assumed that the accuracy of the result isgood.

In order to enable a particularly simple assessment of the results by auser, these can be displayed on a faceplate as shown in FIG. 2, forexample on an operating and monitoring console of a process-engineeringinstallation. A bar on the left B1 shows via the height of a bar segmentB11 the currently measured actual value of the outlet temperatureθ_(W,Aus), which in the example shown lies at approximately 60° C. Therange of values starts at the lower end of the bar and ends at the upperend at 100° C. To the right of this bar B1 is a second bar B2 with theaid of which the capacity of the heat exchanger can be assessed by theuser in a simple manner. The range of values of bar B2 matches that ofbar B1. The height of a lower segment of the bar B21 shows the minimumpossible outlet temperature θ_(W,Aus,Neu) of the product when thecondition of the heat exchanger is new. When the condition of the heatexchanger was new, this was calculated with the aid of the effectiveheat transfer coefficient measured at this time and stored. In theexample, this temperature lies at 31.5° C. A segment of the bar B22lying above this shows by its height the reduction in the capacity ofthe heat exchanger that has already occurred as a result of fouling. Thecurrently calculated value of the minimum possible outlet temperatureθ_(W,Aus,Neu) stands in this example at 44.5° C. and thus due to foulingalready lies 13° C. above the corresponding outlet temperature for theheat exchanger when new. A further segment of the bar B23 shows at itsupper end the inlet temperature θ_(W,Ein) of the product, which iscurrently measured at 90° C. The segment of the bar B23 thus correspondsto the adjustment range of the heat exchanger. The height differencebetween the upper limit of bar segment B11 and the upper limit of barsegment B22 which in the example shown totals 15.8° C., shows how largea remaining correcting range is relative to the currently existingoutlet temperature θ_(W,Aus,Aktuell) of the product. In this way, even auser without particular know-how can assess for how much longer the heatexchanger can reliably continue to be operated. In order to make itpossible for the values to be read off accurately on the faceplate, saidvalues are in practice of course also displayed numerically. Thesenumerical displays are, for reasons of clarity, not shown in FIG. 2. Inorder to enable an estimation to be made of the accuracy of thecalculations, the standard deviation and the minimum and maximum valuedetermined in the manner described previously, the number of value pairson which the calculation was based, as well as the number of value pairsin the subset for which the calculated changes in heat content liewithin the predetermined tolerance band, can also be displayednumerically.

The changes in heat content are calculated only for the heat exchangerin a stationary condition. That has the advantage that only equationsfor mass and energy balances in a state of equilibrium have to be used.Consequently, no further-reaching and considerably more complex physicalmodel, with which the dynamic behavior of the process could besimulated, are needed. This advantageously enables a comparativelysimple calculation to be made of the outlet temperature θ_(W,Aus,Min) ofthe product set for maximum flow of the auxiliary medium.

1. A method for determining a cooling capacity of a heat exchanger,comprising: measuring an inlet temperature and an outlet temperature ofthe product whose temperature is to be changed by the heat exchanger;measuring an inlet temperature and an outlet temperature of theauxiliary medium that serves as a cooling or heating medium duringoperation of the heat exchanger in an at least minimum flow condition;calculating a heat transfer coefficient of the heat exchanger as afunction of the measured temperature values; determining that a changein the heat content of the product, a change in the heat content of theauxiliary medium, and an amount of heat transmitted by the heatexchanger, determined with the calculated heat transfer coefficient, arein a relationship within a defined range from which a change in capacityis identified; and displaying the change in capacity in a unit oftemperature to determine a level of fouling within the heat exchanger,wherein to determine that a change in the heat content of the product, achange in the heat content of the auxiliary medium, and an amount ofheat transmitted by the heat exchanger are in a relationship within adefined range the changes determined with a plurality of value pairs(θ_(K,Aus,i), θ_(W,Aus,j)), where θ_(K,Aus,i) is an empirical value ofthe outlet temperature of the auxiliary medium, which value lies betweenthe measured inlet temperature of the auxiliary medium and the measuredinlet temperature of the product, and where θ_(K,Aus,j) is an empiricalvalue of the outlet temperature of the product, which value lies betweenthe measured inlet temperature of the auxiliary medium and the measuredinlet temperature of the product, the change {dot over (Q)}_(K) in theheat content of the auxiliary medium, the change {dot over (Q)}_(W) Q inthe heat content of the product and the amount of heat {dot over (Q)}which can be transmitted by the heat exchanger having the calculatedheat transfer coefficient are calculated, in that from the plurality ofvalue pairs a subset of value pairs is determined for which the twocalculated values of the changes in heat content {dot over (Q)}_(K) and{dot over (Q)}_(W) and the calculated value of the quantity of heat {dotover (Q)} which can be transmitted differ by less than a predeterminablethreshold value and in that, in accordance with a predeterminablestatistical criterion, from the subset a value pair is selected havingthe value to be displayed of the set outlet temperature of the product.2. The method according to claim 1, wherein a standard deviation of thevalues of the outlet temperature of the product in the subset of valuepairs is calculated and displayed.
 3. The method according to claim 1,wherein as a statistical criterion for the selection of a value pair,the arithmetic mean of the values of the outlet temperature of theproduct in the subset of value pairs is calculated.
 4. The methodaccording to claim 3, wherein a standard deviation of the values of theoutlet temperature of the product in the subset of value pairs iscalculated and displayed.
 5. A device for determining a cooling capacityof a heat exchanger, comprising: a plurality of temperature measuringtransducers effective to measure: an inlet temperature of a product tobe changed by the heat exchanger, an outlet temperature of the product,an inlet temperature of the auxiliary medium effective to change theproduct temperature, an outlet temperature of the auxiliary medium, inan at least minimum flow condition; an evaluation device effective forcalculating a heat transfer coefficient of the heat exchanger as afunction of the temperature values and effective for determining that achange in the heat content of the product, a change in the heat contentof the auxiliary medium, and an amount of heat transmitted by the heatexchanger, determined with the calculated heat transfer coefficient, arein a relationship within a defined range from which a change in capacityis identified; and a display device effective to display the change incapacity in a unit of temperature to determine a level of fouling withinthe heat exchanger, wherein the evaluation device determines, with aplurality of value pairs, (θ_(K,Aus,i), θ_(W,Aus,j)), that a change inthe heat content of the product, a change in the heat content of theauxiliary medium, and an amount of heat transmitted by the heatexchanger are in a relationship within a defined range, whereθ_(K,Aus,i) is an empirical value of the outlet temperature of theauxiliary medium, which value lies between the measured inlettemperature of the auxiliary medium and the measured inlet temperatureof the product, and where θ_(W,Aus,j) is an empirical value of theoutlet temperature of the product, which value lies between the measuredinlet temperature of the auxiliary medium and the measured inlettemperature of the product, the change {dot over (Q)}_(K) in the heatcontent of the auxiliary medium, the change {dot over (Q)}_(W) in theheat content of the product and the amount of heat {dot over (Q)} whichcan be transmitted by the heat exchanger having the calculated heattransfer coefficient are calculated, in that from the plurality of valuepairs a subset of value pairs is determined for which the two calculatedvalues of the changes in heat content {dot over (Q)}_(K) and {dot over(Q)}_(W) and the calculated value of the quantity of heat {dot over (Q)}which can be transmitted differ by less than a predeterminable thresholdvalue and in that, in accordance with a predeterminable statisticalcriterion, from the subset a value pair is selected having the value tobe displayed of the set outlet temperature of the product.